GNGTS 2016 - Atti del 35° Convegno Nazionale

256 GNGTS 2016 S essione 1.3 Viscous dissipation and temperature dependent shear thinning rheology M. Filippucci 1 , A. Tallarico 1 , M. Dragoni 2 1 Dipartimento di Scienze della Terra e Geoambientali, Università degli Studi “Aldo Moro”, Bari, Italy 2 Dipartimento di Fisica e Astronomia, Alma Mater Studiorum - Università di Bologna, Italy Despite the great progresses achieved in numerical modeling, it is not yet possible to completely model a lava flow. The difficulties lie in the fact that the lava is a fluid with extremely complex rheological behavior, given the dependence, usually non-linear, of viscosity on temperature, on the crystal and bubble content and on the strain rate. Moreover, the cooling mechanism is the result of different thermal exchanges both external (surface thermal radiation, forced convection, conduction to the base) and internal (axial advection, viscous dissipation, latent heat, internal conduction). During the flow, the mechanical energy necessary for deformation and flow is dissipated and converted in internal energy, which increases and causes a temperature rise. Recently, a few attempts have been made to model the viscous dissipation in the heat equation and it has been shown that viscous heating can decrease the flow thickness and increase the flow velocity (Piombo and Dragoni, 2011), it can generate a local increase in temperature with consequent decrease of the fluid viscosity (Costa and Macedonio, 2003) and can trigger and sustain secondary rotational flows (Costa and Macedonio, 2005). In this study, we numerically solve the dynamic and heat equations with a shear thinning viscosity dependent on temperature, including the viscous dissipation term in the heat equation. The fluid flows in the x direction in a rectangular channel of width a =3m thickness h =1.5m and length L =50 m, inclined with slope α and with the cross section parallel to the yz plane. The flow is assumed laminar and subjected to the gravity force. We assume a no-slip at the solid boundary and that pressure changes are negligible with respect to body forces. We consider heat advection in the flow direction x and viscous dissipation. Temperature T e at the inflow surface of the lava flow is assumed constant and equal to the effusion temperature. The fluid is assumed isotropic, incompressible, with constant density, thermal conductivity, and specific Fig. 1 – Reynolds number Re at the steady state for effusion temperature T e =1000 °C and α =20° for the case study with viscous dissipation. a) Contour maps of Re on the channel surface z =0; b) contour maps of Re on the channel bottom surface z =- h ; c) contour maps of Re on the channel levee surface y =± a /2. Color gray indicates areas where Re > Re c .; d) Vertical profile of Re at the channel outflow boundary ( x=L , y =0); (e) horizontal profile of Re at the channel outflow boundary ( x=L , z=0.5 m). Dashed lines indicate the value Re c =2000.